The semi-continuous quadratic mixture design problem is a bi-objective problem where the best robust design of a product has to be found. The design is based on mixing raw materials, subject to quadratic constraints and semi-continuity of the variables. The Pareto solution minimizes both the cost and the number of used raw materials. In the Quadratic Bi-Blending (QBB) problem, the Pareto front is determined by the simultaneous design of two products sharing raw materials, with their material availability limits. A specific Branch-and-Bound (B\&B) algorithm for the QBB problem implies two B\&B algorithms, one for each product, sharing the Pareto front and capacity constraints. In this way, the dimension of the search region for each B\&B procedure is smaller than the combined search space. The algorithm aims at finding all solutions and determining the subspace where better designs can be found using higher accuracy of the solutions. The most time consuming part of the procedure is the combination of the finally obtained feasible sets of the two products. Here, we investigate a new B\&B search strategy for QBB problems. The strategy performs a stepwise search with an iteratively increasing accuracy. Experimental results show an average improvement of $32\%$ in the execution time when several combination steps are done, instead of just the final one. Additionally, a parallel version is presented, showing a better improvement in the execution time.